This doesn't even address the conflicting emotions I have about the whole thing.
As a kid Mom would tell me she wanted a chicken to cook so I'd go get one and process it to the point it was plucked and gutted. That doesn't mean I ever enjoy the killing part, even if it is a chicken that has caused problems. I don't enjoy it but I wouldn't keep chickens if I wasn't going to eat them. I mostly hatch my own so they would never have lived to start with.
I don't know if this helps but your chickens have had a great life up until the point they had a bad moment. That's part of your effort on this thread, to make that bad moment as short as you can. Unless you are willing to give up eating meat and such I don't know how you could do it any better.